Figure $3.$ Schematic representation of the system Do the following steps symbolically, do not substitute the actual numerical values until the very end. $2\mathrm{.}1.$ Draw the free body diagram for the ball. Write the Newton's second law for the ball, obtain the nonlinear equation of motion of the system. $2\mathrm{.}2.$ Linearize the equation and take the Laplace transform to obtain the transfer function $($X$($s$))/($theta$($s$)^(**)).2\mathrm{.}3.$ So far, you have obtained the plant transfer function. This plant is controlled by a positioncontrolled servo motor as the actuator. Include the following transfer function of the servo motor to your model: G$\_($a$)($s$)=(2)/(0\mathrm{.}01$ s$+1)$

Figure $3.$ Schematic representation of the system

Do the following steps symbolically, do not substitute the actual numerical values until the very end.

$2\mathrm{.}1.$ Draw the free body diagram for the ball. Write the Newton's second law for the ball, obtain the nonlinear equation of motion of the system.

$2\mathrm{.}2.$ Linearize the equation and take the Laplace transform to obtain the transfer function $\frac{x(s)}{(s)}.$

$2\mathrm{.}3.$ So far, you have obtained the plant transfer function. This plant is controlled by a positioncontrolled servo motor as the actuator. Include the following transfer function of the servo motor to your model:

$G_a(s)=\frac{2}{0\mathrm{.}01s+1}$